For what may be the first time, outside groups — nominally independent spenders that are free from contribution limits and can sometimes conceal their donors from the public — are outspending the parties and candidates in the battle for control of the U.S. Senate, according to a new analysis from the Brennan Center for Justice at NYU School of Law. While closely tied to the parties and candidates despite weak rules against coordination, these groups benefit from being able to raise most of their money from a handful of mega-donors.

Of the $557 million spent so far in ten key Senate contests, nonparty outside groups are responsible for $282 million, or 51 percent. In each of the four most expensive contests, in Nevada, New Hampshire, Ohio, and Pennsylvania, candidates account for 37 percent or less of total spending. Among the other findings:

• Outside spending is reaching record highs: The current record-holder for most expensive race is the 2014 North Carolina contest, which reached $39 million by the end of September and $116 million in total. Four contests are already on pace to beat that mark: Pennsylvania ($69 million by the end of September); Ohio ($49 million); New Hampshire ($48 million); and Nevada ($43 million).

• Party-affiliated groups are ascendant: Due to increased spending by outside groups affiliated with the parties, 2014’s rise of single-candidate groups has been checked. The $28 million spent this year by those groups accounts for 11 percent of the total, down from 18 percent in 2014.

“The precipitous rise of outside groups is problematic for a few reasons,” said author Ian Vandewalker, counsel in the Brennan Center’s Democracy Program. “Unlike the parties and candidates, they are free to accept donations of unlimited size and can conceal their funders from the public. So the bigger a role they play in an election, the more political power is concentrated in the hands of a few million-dollar funders and professional political operatives, with a consequent loss in power for the millions of Americans who can’t afford jumbo donations. While this problem was created in part by 2010’s Citizens United decision, the 2016 data shows we have truly crossed a new Rubicon.”